Optimal and robust design of docking blocks with uncertainty

The positioning and stiffness allocation of docking blocks are an important decision when docking a ship. In this paper, the issues of both optimal design and robust design of docking blocks with uncertainty are discussed, and the corresponding mathematical models are proposed. To describe the uncertainties of various parameters, the proposed method employs the convex model in which the indeterminacy about the uncertain variables is expressed in terms of some sets to which these uncertain variables belong. In the optimisation of docking blocks, the factors considered include the uncertain ship girder loads and uncertain equivalent stiffnesses of blocks. Numerical examples show that uncertainties do affect the optimal solution and lead to an increase in volume of blocks compared to that from deterministic optimisation. A method of robust design with respect to the uncertain equivalent stiffnesses of blocks is also proposed. The robustness of the objective function is achieved by minimising the maximum value of unsatisfactory degree functions of the uncertainty parameters while the feasibility robustness is ensured by an optimisation conducting the worst-case analysis at a lower level. Numerical simulations show that the optimal result from minimisation of the maximum value of unsatisfactory degree functions is superior to that from direct maximisation of the minimum value of uncertainty parameters without the use of unsatisfactory degree functions.